Elaborating slightly (although in general I agree).
Northern states gained power, passed some opressive tarifs/taxes that forced southern states to sell things to the north at the norths price.
The northern states were growing faster in population and number due to a combination of geography (southwest is desert, north west is plains and mountains so guess where the settlers went) and society (in the south the low paying jobs were all taken due to slave labour, in the north low paying jobs got vacated due to greater opportunities to move on to mid-paying jobs or just going west, so guess where new immigrants went to get their feet under them). More people translated into more votes (slightly mitigated in Senate) and thus more political influence over the federal government. The fear was that this would translate to the North imposing various policies that would upset the Southern economy and society (which was pretty much inevitable).
Southern states said "Fuck you."
The Southern states took the opinion that the Union was an alliance of independent states and that if the federal government grew to objectionable then they could opt out and go their own way.
North said "No, fuck you."
The Northern states took the opinion that the Union was a single nation to which the Southern states had sworn allegiance and were now back tracking on that oath.
Both sides raised huge armies and found out the hard way that open field tactics don't work well against rapid-firing rifles. The Union strategy was to blockade the Southern ports, crippling their economy and run the major attacks down the eastern seaboard towards the Confederate capital at Richmond and down the Mississipi (how do you stop writing that?) valley, cutting Texas away and cutting any chance to trade through Mexico. The Confederates mostly tried to block them, occasionally marching north to try to break Union morale and convince them to go home. The Eastern campaigns tended to involve Union armies taking nasty losses against Confederate defenses and going home to rest up. In the West, things went better for the Union and they eventually managed to link up with landings around New Orleans.
Lincon freed all slaves in the CFA. (He didn't free those in the four Union slave states, fucking biased curiculum)
After Gettysburg, a major defensive victory for the Union, Lincoln declared all slaves in the Confederacy to be free in order to further damage the Confederate economy (akin to bombing factories) and to get the abolitionists behind him as morale had been looking shaky.
The CFA, underindustrialized, outnumbered, ignored by the international community, lost.
Lincoln brought Grant, a successful western general, to command the eastern campaign whereupon Northern casualties skyrocketed but since Grant didn't turn round and go home when he got bloodied, the Confederates couldn't keep up the pace and got pushed back while the western armies pillaged their way eastwards behind them. General Lee surrendered, President Davis was captured, President Lincoln got shot.
Northern policy on reunification was about the same as what happened to Germany after WW-I.? (And the idiots say you can't learn anything from history)
The South was broken into districts and placed under martial law until acceptably obedient state governments could be formed. What was left of their economy tanked and their politicians took decades to get back to having any say in the running of the country.
